Open AccessQueues with Dropping Functions and General Arrival Processes
Author(s) -
Andrzej Chydziński,
Pawel Mrozowski
Publication year - 2016
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0150702
Subject(s) - queueing theory , autocorrelation , queue , computer science , function (biology) , markovian arrival process , process (computing) , layered queueing network , probability generating function , mathematics , mathematical optimization , probability distribution , real time computing , moment generating function , statistics , computer network , evolutionary biology , biology , operating system
In a queueing system with the dropping function the arriving customer can be denied service (dropped) with the probability that is a function of the queue length at the time of arrival of this customer. The potential applicability of such mechanism is very wide due to the fact that by choosing the shape of this function one can easily manipulate several performance characteristics of the queueing system. In this paper we carry out analysis of the queueing system with the dropping function and a very general model of arrival process—the model which includes batch arrivals and the interarrival time autocorrelation, and allows for fitting the actual shape of the interarrival time distribution and its moments. For such a system we obtain formulas for the distribution of the queue length and the overall customer loss ratio. The analytical results are accompanied with numerical examples computed for several dropping functions.